# matrices – Checking if a given matrix is orthogonal

Given an orthogonal matrix

$$A= begin{pmatrix} 1 & 1 & 1 &1 \ 1 & 1 & -1 &-1\ 1 & -1 & 0 &0\ 0 &0&1&-1 end{pmatrix}$$

then values of $$[AA^{T}]^{-1}$$ is ?

My question is how come it is an orthogonal matrix $$1^2+1^2+1^2+1^2ne1$$

Sum of squares of rows should be one isnt it?